Supersolvability and nilpotency in terms of the commuting probability and the average character degree

2023/01/18 by Juan José Prieto Martínez, Martínez, Juan
Engineering · Mathematics · #20E45 (Primary) 20C15 #20F16 #20F18 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2301.07633

openalex publication_date 2023/01/18 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

Abstract

Let p be a prime and let G be a finite group such that the smallest prime that divides |G| is p. We find sharp bounds, depending on p, for the commuting probability and the average character degree to guarantee that G is nilpotent or supersolvable.

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